scholarly journals Inference and decision for set identified parameters using posterior lower and upper probabilities

2011 ◽  
Author(s):  
Toru Kitagawa
Keyword(s):  
Lower And Upper Probabilities

Lower And Upper Probabilities For Multiple Comparisons

2016 ◽  
pp. 1
Author(s):  
Faiza F. El Khafifif ◽  
P. F. P. A. Coolen
Keyword(s):  
Multiple Comparisons ◽  
Lower And Upper Probabilities

Non-parametric prediction of unobserved failure modes

2007 ◽  
Vol 221 (3) ◽  
pp. 207-216
Author(s):  
F. P. A. Coolen
Keyword(s):  
Failure Mode ◽  
Failure Modes ◽  
Lower Probability ◽  
Main Interest ◽  
Multinomial Data ◽  
Probability Of Occurrence ◽  
Lower And Upper Probabilities ◽  
Upper Probability ◽  
Non Parametric

This paper presents the application of a recently developed non-parametric predictive inferential approach for multinomial data to the problem of prediction of occurrence of new failure modes. These inferences are in terms of lower and upper probabilities for the next observation. The lower probability of occurrence of a new failure mode is zero in all cases, as the data never suggest strongly that there have to be further failure modes. The main interest is in the upper probability that the next observed failure is caused by a new failure mode.

IMPRECISE SECOND-ORDER MODEL FOR A SYSTEM OF INDEPENDENT RANDOM VARIABLES

2005 ◽  
Vol 13 (02) ◽  
pp. 177-193 ◽  
Author(s):  
LEV V. UTKIN
Keyword(s):  
Random Variables ◽  
Random Variable ◽  
Second Order ◽  
Independent Random Variables ◽  
Order Model ◽  
First Order ◽  
Probability Bounds ◽  
Uncertainty Model ◽  
Lower And Upper Probabilities ◽  
Interval Valued

A new hierarchical uncertainty model for combining different evidence about a system of statistically independent random variable is studied in the paper. It is assumed that the first-order level of the model is represented by sets of lower and upper previsions (expectations) of random variables and the second-order level is represented by sets of lower and upper probabilities which can be viewed as confidence weights for interval-valued expectations of the first-order level. The model is rather general and allows us to compute probability bounds and "average" bounds for previsions of a function of random variables. A numerical example illustrates this model.

scholarly journals A New Belief Entropy to Measure Uncertainty of Basic Probability Assignments Based on Belief Function and Plausibility Function

Entropy ◽  
2018 ◽  
Vol 20 (11) ◽  
pp. 842 ◽  
Author(s):  
Lipeng Pan ◽  
Yong Deng
Keyword(s):  
Measurement Uncertainty ◽  
Belief Function ◽  
Probability Interval ◽  
Numerical Examples ◽  
Main Work ◽  
Lower And Upper Probabilities ◽  
Basic Probability ◽  
Open Issue ◽  
Belief Entropy ◽  
Deng Entropy

How to measure the uncertainty of the basic probability assignment (BPA) function is an open issue in Dempster–Shafer (D–S) theory. The main work of this paper is to propose a new belief entropy, which is mainly used to measure the uncertainty of BPA. The proposed belief entropy is based on Deng entropy and probability interval consisting of lower and upper probabilities. In addition, under certain conditions, it can be transformed into Shannon entropy. Numerical examples are used to illustrate the efficiency of the new belief entropy in measurement uncertainty.

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